Lineage

As he was under the Wila' of Banu Asad, he is called al-Asadi, and because he and his family lived in Kufa, he is called al-Kufi. Muwahhid Abtahi said perhaps Husayn b. Mansur al-Asadi al-Kufi which is mentioned as a reliable (Thiqa) narrator in Sunni Rijal sources is his father; although Shi'a Rijal sources did not mention him.

In available versions of Khulasat al-aqwal, his father's named is mistakenly recorded as Husayn (Arabic: حسین).

There is another Dawud b. Husayn which is mentioned in Sunni Rijal sources, who is definitely another person.

Reliability

Opinions of al-Tusi and al-Najashi

While al-Najashi said that he was Thiqa (reliable), Ibn 'Uqda and al-Shaykh al-Tusi said that he was Waqifi. This led to a disagreement among later Rijal scholars about the reliability of Dawud.

Disagreement among Rijal Scholars

Ibn Dawud al-Hilli has listed him once among the praised narrators based on al-Najashi's saying, and once among the dispraised narrators based on al-Shaykh al-Tusi's saying. Al-'Allama al-Hilli has also mentioned him in the second part of his book which contains the name of narrators that he did not trust.
Although Mirdamad claimed that al-'Allama al-Hilli regarded the Hadiths narrated by Dawud as Sahih, by referring to 'Allama's saying it appears that he said the path of a Hadith is Sahih (correct) to Dawud, but not the Hadith itself.

Preferring al-Tusi's Opinion

Some scholars have preferred the opinion of al-Shaykh al-Tusi over the al-Najashi's, and consequently believed that the Hadiths narrated by him are Da'if (weak). On the other hand, some said that there is no contradiction between these two opinions and Dawud b. Husayn is simply a reliable (Thiqa) non-Twelver narrator.

Preferring al-Najashi's Opinion

Nevertheless, some have chosen the opinion of al-Najashi, as it is stronger than al-Tusi's. Moreover, Wahid Bihbahani said the narration of Safwan b. Yahya, Ahmad b. Muhammad b. Abi Nasr al-Bazanti and other reliable Muhaddiths such as Ja'far b. Bashir form Dawud b. Husayn supports the opinion of al-Najashi. He doubted that Dawud was Waqifi and said that al-Shaykh al-Tusi has taken his opinion from Ibn 'Uqda, who was a member of Jarudiyya until his death, thus his opinion is invalid.
However, this is not acceptable as it means al-Tusi simply followed Ibn 'Uqda without knowing the truth. In addition, Ibn 'Uqda was a reliable Muhaddith and his opinions are valid.
On the other hand, Mirdamad claimed that there is consensus on his reliability and the report that he was Waqifi has not been proven.
Dawud b. Husayn had a book, to which al-Najashi mentioned a path and al-Tusi mentioned two paths.

His Hadiths

Most of Hadiths narrated form Dawud are related to different jurisprudential topics, such as: fasting, Hajj, marriage and divorce. Hadiths about the right of a faithful on another faithful, Occultation of Imam al-Mahdi (a) and exegesis of the Holy Qur'an has been narrated from him. It is noteworthy, that he has narrated the famous Hadith from 'Umar b. Hanzala about the disagreement in Hadiths.

References

The material for this article is mainly taken from داوود بن حصین in Farsi WikiShia.